Question

Which of the following is the second derivative of the function f(x)=x^3+1/3x

Answer 1

2x^3 + 2 / 3x^3 that’s the answer

Answer 2

`f(x)=\cfrac{x^3+1}{3x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{quotient rule}}{\cfrac{(3x^2)(3x)-(x^3+1)(3)}{9x^2}}\implies \cfrac{9x^3-3x^3-3}{9x^2}\implies \stackrel{\textit{1st derivative}}{\cfrac{6x^3-3}{9x^2}} \\\\[-0.35em] ~\dotfill`

`\stackrel{\textit{quotient rule}}{\cfrac{(18x^2)(9x^2)-(6x^3-3)(18x)}{81x^4}}\implies \cfrac{162x^4-108x^4+54x}{81x^4}\implies \cfrac{54x^4+54x}{81x^4} \\\\\\ \cfrac{54x(x^3+1)}{81x^4}\implies \cfrac{2(x^3+1)}{3x^3}\implies \stackrel{\textit{2nd derivative}}{\cfrac{2x^3+2}{3x^3}}`